Monte Carlo (MC) simulation has been recognized as the most accurate dose calculation method for radiotherapy. However, the extremely long computation time impedes its clinical application. Recently, a lot of effort has been made to realize fast MC dose calculation on graphic processing units (GPUs). However, most of the GPU-based MC dose engines have been developed under NVidia's CUDA environment. This limits the code portability to other platforms, hindering the introduction of GPU-based MC simulations to clinical practice. The objective of this paper is to develop a GPU OpenCL based cross-platform MC dose engine named goMC with coupled photon-electron simulation for external photon and electron radiotherapy in the MeV energy range. Compared to our previously developed GPU-based MC code named gDPM (Jia et al 2012 Phys. Med. Biol. 57 7783-97), goMC has two major differences. First, it was developed under the OpenCL environment for high code portability and hence could be run not only on different GPU cards but also on CPU platforms. Second, we adopted the electron transport model used in EGSnrc MC package and PENELOPE's random hinge method in our new dose engine, instead of the dose planning method employed in gDPM. Dose distributions were calculated for a 15 MeV electron beam and a 6 MV photon beam in a homogenous water phantom, a water-bone-lung-water slab phantom and a half-slab phantom. Satisfactory agreement between the two MC dose engines goMC and gDPM was observed in all cases. The average dose differences in the regions that received a dose higher than 10% of the maximum dose were 0.48-0.53% for the electron beam cases and 0.15-0.17% for the photon beam cases. In terms of efficiency, goMC was ~4-16% slower than gDPM when running on the same NVidia TITAN card for all the cases we tested, due to both the different electron transport models and the different development environments. The code portability of our new dose engine goMC was validated by successfully running it on a variety of different computing devices including an NVidia GPU card, two AMD GPU cards and an Intel CPU processor. Computational efficiency among these platforms was compared.